Optimal inspection of imports to prevent invasive pest introduction
The U.S. horticulture industry imports over one billion live plants annually, an important and growing pathway for the introduction of damaging non-native insects and diseases. One means for reducing the introduction of invasive pests is the inspection of imported shipments of live plants and treatment, rejection, or destruction of shipments found infested. In this work we identify optimal inspection strategies for allocating a fixed inspection budget across incoming, heterogeneous shipments to minimize pest introduction. We derive a formula for slippage -- the expected number of accepted infested plant units in a shipment -- dependent on shipment size, sample size, infestation rate, and detection rate. Slippage is an indicator of pest propagule pressure, a key determinant of pest establishment; thus, minimizing slippage across imports is important for phytosanitary protection. We therefore formulate and analyze an inspector's optimization problem to minimize total expected slippage across shipments and conduct an empirical analysis of inspecting live plant imports. We develop maximum likelihood estimates of the underlying infestation rates of imported plant genera from historic inspection data, and we compare derived optimal inspection strategies to those historically and currently employed to evaluate their effectiveness for preventing pest introduction.
We find that slippage-minimizing inspection strategies target the subset of largest and dirtiest shipments (i.e., shipments with the highest expected slippage). Further, such strategies yield substantial reductions in expected slippage relative to historic and current inspection strategies, which sample a fixed proportion of each shipment or aim to achieve a consistent detection level across all shipments. Recognizing that USDA-APHIS may want to ensure that all shipments are sampled at least at a baseline level and that such comprehensive sampling is needed to provide data from which to estimate infestation rates of live plant pathways, we also consider how additional sampling capacity, beyond a baseline survey effort, could be allocated across imported shipments to minimize total expected slippage. We find that allocating additional sampling capacity to the largest, dirtiest shipments can substantially reduce expected slippage relative to the baseline sampling effort. As such, the dual goals of minimizing the number of accepted infested plants and maintaining a baseline sampling effort may be able to be met without substantial compromise, and may be an important strategy for reducing the introduction of invasive pests from trade.